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<p>&nbsp;<p>
<hr noshade size="5">
<h2><a name="AbelianFieldToRCF"></a>
AbelianFieldToRCF
</h2>

Computes the data neccessary to get an abelian field as a Ray Class Field.

<p><p>

<h3>
Syntax:
</h3>
<pre>rc := AbelianFieldToRCF(o [, I]);</pre>

<p>

<table>
<tr>
<td>list</td>
<td><pre>  rc  </pre></td>
<td>[ ideal, inf, relations ]</td>
</tr>
<tr>
<td>order</td>
<td><pre>  o  </pre></td>
<td>of an abelian field with known automorphisms</td>
</tr>
<tr>
<td>ideal</td>
<td><pre>  I  </pre></td>
<td>of the coef. ring of <tt> o</tt>. Must be a multiple of the conductor.</td>
</tr>
</table>

<p>


<h3>
Description:
</h3>
<i>no detailed description available yet</i>

<p><p>

<p>
<hr>
<p>
<h3>
Example:
</h3>
Suppose we know that the field generated by a root of x^4-4x^2+1
is abelian, and we'd like to work with this field:
<pre>

kash> o := OrderMaximal(x^4-4*x^2+1);
Generating polynomial: x^4 - 4*x^2 + 1
Discriminant: 2304 

kash> OrderAutomorphisms(o);
[ [0, 1, 0, 0], [0, -4, 0, 1], [0, 4, 0, -1], [0, -1, 0, 0] ]
kash> rc1 := AbelianFieldToRCF(o, Disc(o));
Quotient of RayClassGroupToAbelianGroup(<2304>, [  ])
Group with relations:
[  2   0]
[  0   2]
[  2   0]
[  0 192]
kash> f := RayConductor(rc1);
[ <24>, [  ] ]
kash> rc2 := AbelianFieldToRCF(o, f[1]);
Quotient of RayClassGroupToAbelianGroup(<24>, [  ])
Group with relations:
[2 0]
[0 2]
[2 0]
[0 2]
kash> rcf := RayClassField(rc2);
> [ x^2 - 2, x^2 - 3 ]

</pre>

<p>


<hr>

<p>
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